The instant invention is directed to a method and apparatus for predicting wavelength dependent radiation influences in thermal systems, and more particularly for predicting such influences in systems including semitransparent mediums in a relatively simply manner such that the predictions can be rapidly carried out. The predictive system includes a model which may be executed quickly on workstation class computing platforms and may be used, for example, in the design and control of rapid thermal processing (RTP) systems by permitting rapid comparison of alternative reactor designs and physical models as well as real-time model-based control procedures.
Prior attempts to simulate complex thermal systems such as RTP reactors have generally followed two approaches. In a first approach two-dimensional and three-dimensional finite-element or finite-volume approaches have been used to model the heat transport and coupled fluid flow in the reaction chamber. In such systems, the radiation exchange is handled through radiation view or exchange factors. Such approaches generally consider only gray-diffuse view factors. One approach, described in Lie et al., "Simulation of Thermal Processing Equipment and Processes," Rapid Thermal and Integrated Processing II, Material Research Society Symposium Proceeding, 303 (1993), also considers specular reflection in their exchange factors. Gray-diffuse view factors are calculated by geometry. Typically, the specular exchange factors are calculated using Monte-Carlo, ray-tracing software. Such a modeling technique is disadvantageous in that it is complex and requires a relatively long time to run.
The second approach to RTP modeling is based on process control. In these efforts, the models consider only one-dimensional conduction in the wafer, with convective and radiative heat fluxes considered at the wafer surfaces. The radiation is computed in terms of geometric gray-diffuse view factors that couple the lamp system to the wafer. While such models may be run relatively quick on a computer, and are therefore suitable for use in designing the real-time control algorithms, these approaches do not take into account non-gray wavelength-dependent radiation.
Because radiation is an electromagnetic wave, an accurate model of radiative energy transport must include the influences of spectral (wavelength-dependent) and directional factors. The conventional technique treats radiative heat transfer between surfaces as diffuse reflectors and diffuse emitters-absorbers. In this way, the problem of diffuse surface interchange is reduced to a geometric problem of determining the view factors between all interacting surfaces, and the directional effects are eliminated.
The values of surface radiation properties (emissivity, transmissivity, and reflectivity) depend on the wavelength, thermodynamic state (e.g., temperature and composition or mole numbers) and the morphology of the surface (e.g., surface roughness). In other words, the radiation emitted, reflected, transmitted and absorbed by a solid body depends on the radiative properties of the material, temperature of the body, viewing direction and the surface conditions.
Typically, conventional attempts to solve the complexity of the radiative transport consider only wavelength-independent radiation (gray-diffuse). Alternatively, some kind of indirect way to estimate roughly the wavelength-dependent effects is employed. These approaches are not satisfactory, since spectral emissivity plays an important role in the behavior of radiative heat exchange between materials.